메뉴 건너뛰기




Volumn 99, Issue 1, 2004, Pages 175-196

Solving linear programs with finite precision: I. Condition numbers and random programs

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; ITERATIVE METHODS; OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING;

EID: 18144418311     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10107-003-0393-7     Document Type: Article
Times cited : (12)

References (28)
  • 1
    • 0037749334 scopus 로고    scopus 로고
    • A new condition number for linear programming
    • Cheung, D., Cucker, F.: A new condition number for linear programming. Math. Program. 91, 163-174 (2001)
    • (2001) Math. Program. , vol.91 , pp. 163-174
    • Cheung, D.1    Cucker, F.2
  • 2
    • 0036262238 scopus 로고    scopus 로고
    • Probabilistic analysis of condition numbers for linear programming
    • Cheung, D., Cucker, F.: Probabilistic analysis of condition numbers for linear programming. J. Optim. Theory and Appl. 114, 55-67 (2002)
    • (2002) J. Optim. Theory and Appl. , vol.114 , pp. 55-67
    • Cheung, D.1    Cucker, F.2
  • 4
    • 0142055280 scopus 로고    scopus 로고
    • On the expected condition number of linear programming problems
    • Cucker, F., Wschebor, M.: On the expected condition number of linear programming problems. Numer. Math. 94, 419-478 (2003)
    • (2003) Numer. Math. , vol.94 , pp. 419-478
    • Cucker, F.1    Wschebor, M.2
  • 5
    • 0001900752 scopus 로고
    • Maximization of a linear function of variables subject to linear inequalities
    • Tj.C. Koopmans, ed. John Wiley & Sons
    • Dantzig, G.B.: Maximization of a linear function of variables subject to linear inequalities. In Tj.C. Koopmans, ed. Activity Analysis of Production and Allocation, p. 339-347. John Wiley & Sons, 1951
    • (1951) Activity Analysis of Production and Allocation , pp. 339-347
    • Dantzig, G.B.1
  • 7
    • 0000324960 scopus 로고
    • Eigenvalues and condition numbers of random matrices
    • Edelman, A.: Eigenvalues and condition numbers of random matrices. SIAM J. Matrix Anal. Applic. 9, 543-556 (1988)
    • (1988) SIAM J. Matrix Anal. Applic. , vol.9 , pp. 543-556
    • Edelman, A.1
  • 8
    • 0142033061 scopus 로고    scopus 로고
    • Pre-conditioners and relations between different measures of conditioning for conic linear systems
    • Freund, R., Epelman, M.: Pre-conditioners and relations between different measures of conditioning for conic linear systems. MIT Operations Research Center Working Paper OR-344-00, 2000
    • (2000) MIT Operations Research Center Working Paper , vol.OR-344-00
    • Freund, R.1    Epelman, M.2
  • 9
    • 0033261317 scopus 로고    scopus 로고
    • Condition-based complexity of convex optimization in conic linear form via the ellipsoid algorithm
    • Freund, R.M., Vera, J.R.: Condition-based complexity of convex optimization in conic linear form via the ellipsoid algorithm. SIAM J. Optim. 10, 155-176 (1999)
    • (1999) SIAM J. Optim. , vol.10 , pp. 155-176
    • Freund, R.M.1    Vera, J.R.2
  • 10
    • 0000553640 scopus 로고    scopus 로고
    • Some characterizations and properties of the distance to ill-posedness and the condition measure of a conic linear system
    • Freund, R.M., Vera, J.R.: Some characterizations and properties of the distance to ill-posedness and the condition measure of a conic linear system. Math. Program. 86, 225-260 (1999)
    • (1999) Math. Program. , vol.86 , pp. 225-260
    • Freund, R.M.1    Vera, J.R.2
  • 12
    • 0003258173 scopus 로고    scopus 로고
    • Accuracy and stability of numerical algorithms
    • Higham, N.: Accuracy and Stability of Numerical Algorithms. SIAM, 1996
    • (1996) SIAM
    • Higham, N.1
  • 13
    • 51249181779 scopus 로고
    • A new polynomial time algorithm for linear programming
    • Karmarkar, N.: A new polynomial time algorithm for linear programming. Combinatorica 4, 373-395 (1984)
    • (1984) Combinatorica , vol.4 , pp. 373-395
    • Karmarkar, N.1
  • 14
    • 0000564361 scopus 로고
    • A polynomial algorithm in linear programming
    • Khachijan, L.G.: A polynomial algorithm in linear programming. Dokl. Akad. Nauk SSSR 244, 1093-1096 (1979);
    • (1979) Dokl. Akad. Nauk SSSR , vol.244 , pp. 1093-1096
    • Khachijan, L.G.1
  • 15
    • 0018454236 scopus 로고
    • In Russian, English translation in
    • In Russian, English translation in Soviet Math. Dokl. 20, 191-194 (1979)
    • (1979) Soviet Math. Dokl. , vol.20 , pp. 191-194
  • 16
    • 0001849163 scopus 로고
    • How good is the simplex method
    • O. Shisha, ed. Academic Press
    • Klee, V., Minty, G.J.: How good is the simplex method. In O. Shisha, ed, Inequalities III, p. 159-175. Academic Press, 1972
    • (1972) Inequalities III , pp. 159-175
    • Klee, V.1    Minty, G.J.2
  • 17
    • 84949482231 scopus 로고
    • Is it possible to know a problem instance is ill-posed?
    • Renegar, J.: Is it possible to know a problem instance is ill-posed? J. Complex. 10, 1-56 (1994)
    • (1994) J. Complex. , vol.10 , pp. 1-56
    • Renegar, J.1
  • 18
    • 0028426653 scopus 로고
    • Some perturbation theory for linear programming
    • Renegar, J.: Some perturbation theory for linear programming. Math. Program. 65, 73-91 (1994)
    • (1994) Math. Program. , vol.65 , pp. 73-91
    • Renegar, J.1
  • 19
    • 0000208672 scopus 로고
    • Incorporating condition measures into the complexity theory of linear programming
    • Renegar, J.: Incorporating condition measures into the complexity theory of linear programming. SIAM J. Optim. 5, 506-524 (1995)
    • (1995) SIAM J. Optim. , vol.5 , pp. 506-524
    • Renegar, J.1
  • 20
    • 0029195774 scopus 로고
    • Linear programming, complexity theory and elementary functional analysis
    • Renegar, J.: Linear programming, complexity theory and elementary functional analysis. Math. Program. 70, 279-351 (1995)
    • (1995) Math. Program. , vol.70 , pp. 279-351
    • Renegar, J.1
  • 21
    • 0000685126 scopus 로고
    • On scaled projections and pseudoinverses
    • Stewart, G.W.: On scaled projections and pseudoinverses. Linear Algebra Appl. 112, 189-193 (1989)
    • (1989) Linear Algebra Appl. , vol.112 , pp. 189-193
    • Stewart, G.W.1
  • 22
    • 0025512866 scopus 로고
    • A Dantzig-Wolfe-like variant of Karmarkar's interior-point linear programming algorithm
    • Todd, M.J.: A Dantzig-Wolfe-like variant of Karmarkar's interior-point linear programming algorithm. Oper. Res. 38, 1006-1018 (1990)
    • (1990) Oper. Res. , vol.38 , pp. 1006-1018
    • Todd, M.J.1
  • 23
    • 0003079802 scopus 로고    scopus 로고
    • Characterizations, bounds and probabilistic analysis of two complexity measures for linear programming problems
    • Todd, M.J., Tunçel, L., Ye, Y.: Characterizations, bounds and probabilistic analysis of two complexity measures for linear programming problems. Math. Program. 90, 59-69 (2001)
    • (2001) Math. Program. , vol.90 , pp. 59-69
    • Todd, M.J.1    Tunçel, L.2    Ye, Y.3
  • 24
    • 0029313616 scopus 로고
    • Condition numbers for polyhedra with real number data
    • Vavasis, S.A., Ye, Y.: Condition numbers for polyhedra with real number data. Oper. Res. Lett. 17, 209-214 (1995)
    • (1995) Oper. Res. Lett. , vol.17 , pp. 209-214
    • Vavasis, S.A.1    Ye, Y.2
  • 25
    • 30244506467 scopus 로고    scopus 로고
    • A primal-dual interior point method whose running time depends only on the constraint matrix
    • Vavasis, S.A., Ye, Y.: A primal-dual interior point method whose running time depends only on the constraint matrix. Math. Program. 74, 79-120 (1996)
    • (1996) Math. Program. , vol.74 , pp. 79-120
    • Vavasis, S.A.1    Ye, Y.2
  • 26
    • 0001249354 scopus 로고    scopus 로고
    • Primal-dual interior-point methods
    • Wright, S.: Primal-Dual Interior-Point Methods. SIAM, 1997
    • (1997) SIAM
    • Wright, S.1
  • 27
    • 0002953043 scopus 로고
    • Toward probabilistic analysis of interior-point algorithms for linear programming
    • Ye, Y.: Toward probabilistic analysis of interior-point algorithms for linear programming. Math. Oper. Res. 19, 38-52 (1994)
    • (1994) Math. Oper. Res. , vol.19 , pp. 38-52
    • Ye, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.